In Section 3 we consider how to sketch the graphs of more complicated functions, sometimes involving trigonometric functions. We look at graphs which are sums, quotients and composites of different functions, and at those which are defined by a different rule for different values of x.

Click 'View document' below to open Section 3 (7 pages, 133KB).

Earlier you looked at place values for numbers, and why they were called powers of ten.

Place value10 0001000100101Author(s): The Open University

1 What are the following?

• (a) 10

• (b) 01

• (c) 20

• (d) 02

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1 Write the following as a number to a single power:

• (a) 26 Ã· 22

• (b) 1010 Ã· 107

• (c) 78 Ã· 74

• Author(s): The Open University

Given any number, you now know how to find its square. But, given the squared number, how do you find the original number?

## Example 3

1 Write down the coordinates of the point P on each of the graphs below and interpret these coordinates in terms of the labels on the axes.

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1 On the plan of the bathroom in Example 1, what is the width of the window and
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The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. Once you have completed the workbook and exercises return to this page and watch the video below, â€˜The arch never sleepsâ€™, which discusses a practical application of some of the ideas in workbook.

Click 'View document' to open the workbook (PDF, 0.8
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Assuming that both the content of mathematics and the processes need to be included in programmes and curricula, the problem becomes one of how a suitable curriculum can be structured. One possibility is to construct a very specific curriculum with clearly defined objectives for both content and processes separately, and possibly with suggested learning activities. However, content and process are two complementary ways of viewing the subject.

An alternative is to see the curriculum in
Author(s): The Open University

After studying this unit you should:

• be able to perform basic algebraic manipulation with complex numbers;

• understand the geometric interpretation of complex numbers;

• know methods of finding the nth roots of complex numbers and the solutions of simple polynomial equations.

Author(s): The Open University

Mailing or discussion lists are email-based discussion groups. When you send an email to a mailing list address, it is sent automatically to all the other members of the list.

The majority of academic-related mailing lists in the UK are maintained by Jiscmail. You will find details of joining these mailing lists on the Jiscmail website. Mailing lists are useful for getting in touch with like-minded colleagues. They are also handy for keeping up to date with current thinking and research
Author(s): The Open University

Referencing is not only useful as a way of sharing information, but also as a means of ensuring that due credit is given to other peopleâ€™s work. In the electronic information age, it is easy to copy and paste from journal articles and web pages into your own work. But if you do use someone elseâ€™s work, you should acknowledge the source by giving a correct reference.

Taking someone's work and not indicating where you took it from is termed plagiarism and is regarded as an infringemen
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An original piece of work, whether it is text, music, pictures, sound recordings, web pages, etc., is protected by copyright law and may often have an accompanying symbol (Â©) and/or legal statement. In the UK it is the Copyright, Designs and Patents Act 1988 which regulates this.

In most circumstances, works protected by copyright can be used in whole or in part only with the permission of the owner. In some cases this permission results in a fee.

However, the UK legislation incl
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If you find you have a long unmanageable list of favourites/bookmarks you might like to try social bookmarks as an alternative.

## Activity â€“ what you need to know about social bookmarks

Read 7 things you should know about soci
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1.5.4The 5 Ds

If you donâ€™t use a system at all, then you could suffer from the effects of information overload:

• losing important information

• wasting time on trying to find things

• ending up with piles of physical and virtual stuff everywhere

One technique you might like to apply to your files (be they paper or electronic) is the 5Ds. Try applying these and see if you can reduce your information overload.

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1.5.3 Desktop search tools

Finding your paperwork or electronic files can be a problem. You may find that even if you do have some sort of filing system, your structure soon gets quite large with files in multiple locations, which can be hard to navigate. You may find yourself making arbitrary decisions about which folder to place a document in. It may make sense now but in the future, when you look where you think it should be, itâ€™s not there.

At times like this you may resort to the search command from the Wi
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1.5.2 Ways of organising yourself

How do you organise yourself?

## Activity

Make a note of how you organise your:

• emails

• internet bookmarks or favorites

• computer files

• your
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1.3.8 Choosing the right tool for the job

Before searching it is always a good idea to check what the source you have chosen covers to make sure it will unearth information that matches your search need (you will notice that all the resources weâ€™ve covered in this guide have short descriptions to enable you to decide which to use). Some of the decision makers, depending on the context of your search might be:

• Does it have full text?

• Does it cover the right subject?

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4.4 Signing everyone up to sustainability

The proposers of step-by-step progress towards sustainability would include in their plans many of the ideas proposed in the previous two subsections. However, what distinguishes this group is that they stand in the middle of the scale between faith in unfettered business voluntarism and a conviction that radical transformations are required. Their incrementalism is reflected in the kinds of pragmatic solutions they propose; their radicalism shows in the way they think about new roles and pro
Author(s): The Open University

5.1 Actions for lighter living

Nobody made a greater mistake than he who did nothing because he could only do little.

(Edmund Burke, 1729â€“1797)

If you want to consider how to further lighten your carbon footprint, you may need more detailed information on the effect of technical and behavioural actions not covered by the carbon calculator, or included only as a part of other actions.

It's important to understand whic
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